An efficient comparison of average run length approximation methods of exponentially weighted moving average control chart when observations are binomial distributed by Monte Carlo simulation and Markov Chain approach
Abstract:
The objective of this paper is to study the approximation methods of Average Run Length (ARL) for detection an increasing a proportion of defective with Exponentially Weighted Moving Average (EWMA) chart by Markov Chain Approach (MCA). The accuracy of results is compared with the results obtained from Monte Carlo simulation (MC). The Markov Chain Approach with EWMA chat can be obtained ARL for detection of changes must faster than Monte Carlo simulation when fixed a magnitude of changes and incontrol (ARL (ARL0). The sample sizes of this study are 30, 50 and 100 and defective proportion for the case of incontrol state is α (ARL0 ) = 0.01 and increase the defective proportions from up 1% to 10% for the case of outofcontrol state. Although this method is as accurate and valid as the traditional method, the advantage of this method uses time less than traditional method as seen simulations in this study.